3. Actually they tried 'rebranding' last time. 'We are now the Tea Party'.....

it didn't really work all that well. But after Bush and the blows to GOP public image, the 'Tea Party' ploy was an attempt to engage in Republican politics under a name that was not 'Republican'. Of course the 'Tea Party' never even tried to be a real Party, they were always just a subset of the Republican Party, the subset that tried to get others involved by pretending they were not part of the mainstream Party of GW Bush.
They tried rebranding, and it backfired on them.